A G matrix analogue to capture the cumulative effects of nongenetic inheritance

The genetic variance‐covariance ( G ) matrix describes the variances and covariances of genetic traits under strict genetic inheritance. Genetically expressed traits often influence trait expression in another via nongenetic forms of transmission and inheritance, however. The importance of non‐genetic influences on phenotypic evolution is increasingly clear, but how genetic and nongenetic inheritance interact to determine the response to selection is not well understood. Here, we use the ‘reachability matrix’ – a key analytical tool of geometric control theory – to integrate both forms of inheritance, capturing how the consequences of generation‐lagged maternal effects accumulate. Building on the classic Lande and Kirkpatrick model that showed how nongenetic (maternal) inheritance fundamentally alters the expected path of phenotypic evolution, we make novel inferences through decomposition of the reachability matrix. In particular, we quantify how nongenetic inheritance affects the distribution (orientation and shape) of ellipses of phenotypic change and how these distributions influence subsequent evolution. This interweaving of phenotypic means and variances accumulates generation by generation and is described analytically by the reachability matrix, which acts as an analogue of G when genetic and nongenetic inheritance both act.     

How stabilizing selection and nongenetic inheritance combine to shape the evolution of phenotypic plasticity

Relatively little is known about whether and how nongenetic inheritance interacts with selection to impact the evolution of phenotypic plasticity. Here, we empirically evaluated how stabilizing selection and a common form of nongenetic inheritance—maternal environmental effects—jointly influence the evolution of phenotypic plasticity in natural populations of spadefoot toads. We compared populations that previous fieldwork has shown to have evolved conspicuous plasticity in resource‐use phenotypes (“resource polyphenism”) with those that, owing to stabilizing selection favouring a narrower range of such phenotypes, appear to have lost this plasticity. We show that: (a) this apparent loss of plasticity in nature reflects a condition‐dependent maternal effect and not a genetic loss of plasticity, that is “genetic assimilation,” and (b) this plasticity is not costly. By shielding noncostly plasticity from selection, nongenetic inheritance generally, and maternal effects specifically, can preclude genetic assimilation from occurring and consequently impede adaptive (genetic) evolution.     

Mass‐dependent reproductive strategies in wild bighorn ewes: a quantitative genetic approach

In the Ram Mountain bighorn sheep (Ovis canadensis) population, ewes differing by more than 30% in body mass weaned lambs with an average mass difference of only 3%. Variability in adult body mass was partly due to additive genetic effects, but inheritance of weaning mass was weak. Maternal effects could obscure genetic effects in the phenotypic expression of weaning mass, particularly if they reflected strategies of maternal expenditure that varied according to ewe mass. We performed a quantitative genetic analysis to assess genetic and environmental influences on ewe mass and on maternal expenditure. We used the mean daughters/mother regression method and Derivative Free Restricted Maximum Likelihood models to estimate heritability (h²) of ewe mass and indices of maternal expenditure. We found additive genetic effects on phenotypic variation in maternal mass, in lamb mass at weaning (absolute maternal expenditure) and in weaning mass relative to maternal mass at weaning (relative maternal expenditure). Heritability suggests that maternal expenditure has the potential to evolve. The genetic correlation of ewe mass and absolute maternal expenditure was weak, while ewe mass and relative maternal expenditure were strongly negatively correlated. These results suggest additive genetic effects on mass‐dependent reproductive strategies in bighorn ewes. Mass‐dependent reproductive strategies could affect lamb survival and phenotypic variation in adult mass. As population density increased and reproduction became costlier, small females reduced maternal expenditure more than large females. Constraints on reproductive strategy imposed by variations in resource availability are therefore likely to differ according to ewe mass. A general trend for a decrease in maternal expenditure relative to maternal size in mammals suggests that size‐dependent negative maternal effects may be common.     

Effects of maternal and grandmaternal flea infestation on offspring quality and quantity in a desert rodent: evidence for parasite-mediated transgenerational phenotypic plasticity

Parasites can cause a broad range of sublethal fitness effects across a wide variety of host taxa. However, a host’s efforts to compensate for possible parasite-induced fitness effects are less well-known. Parental effects may beneficially alter the offspring phenotype if parental environments sufficiently predict the offspring environment. Parasitism is a common stressor across generations; therefore, parental infestation could reliably predict the likelihood of infestation for offspring. However, little is known about relationships between parasitism and transgenerational phenotypic plasticity. Thus, we investigated how maternal and grandmaternal infestation with fleas (Xenopsylla ramesis) affected offspring quality and quantity in a desert rodent (Meriones crassus). We used a fully-crossed design with control and infested treatments to examine litter size, pup body mass at birth, and pup mass gain before weaning for combinations of maternal and grandmaternal infestation status. No effect of treatment on litter size or pup body mass at birth was found. However, maternal and grandmaternal infestation status significantly affected pre-weaning body mass gain, a proxy for the rate of maturation, in male pups. Pups gained significantly more weight before weaning if maternal and grandmaternal infestation statuses matched, regardless of the treatment. Thus, pups whose mothers and grandmothers experienced similar risks of parasitism, either both non-parasitized or both infested, would reach sexual maturity more quickly than those pups whose mothers’ infestation status did not match that of their grandmothers. These results support the contention that parents can receive external cues such as the risk of parasitism, that prompt them to alter offspring provisioning. Therefore, parasites could be a mediator of environmentally-induced maternal effects and could affect host reproductive fitness across multiple generations.     

When to rely on maternal effects and when on phenotypic plasticity?

Existing insight suggests that maternal effects have a substantial impact on evolution, yet these predictions assume that maternal effects themselves are evolutionarily constant. Hence, it is poorly understood how natural selection shapes maternal effects in different ecological circumstances. To overcome this, the current study derives an evolutionary model of maternal effects in a quantitative genetics context. In constant environments, we show that maternal effects evolve to slight negative values that result in a reduction of the phenotypic variance (canalization). By contrast, in populations experiencing abrupt change, maternal effects transiently evolve to positive values for many generations, facilitating the transmission of beneficial maternal phenotypes to offspring. In periodically fluctuating environments, maternal effects evolve according to the autocorrelation between maternal and offspring environments, favoring positive maternal effects when change is slow, and negative maternal effects when change is rapid. Generally, the strongest maternal effects occur for traits that experience very strong selection and for which plasticity is severely constrained. By contrast, for traits experiencing weak selection, phenotypic plasticity enhances the evolutionary scope of maternal effects, although maternal effects attain much smaller values throughout. As weak selection is common, finding substantial maternal influences on offspring phenotypes may be more challenging than anticipated.     

Negative maternal or paternal effects on tactic inheritance under a conditional strategy

Alternative behavioral and life-history tactics are common in animal populations. The conditional strategy model provides a powerful explanation for the evolution and persistence of such tactics, as it allows alternative tactics to be perpetuated even if there is tactic inheritance and tactics yield unequal mean fitness. In many biological systems negative maternal or paternal effects complicate the inheritance of condition and, hence, the inheritance of alternative tactics. Indeed, the inheritance of condition may result in the alternation of tactics across generations. In this paper, we show that the conditional strategy is robust to these effects on progeny condition. There is a unique and stable proportion of tactics under standard inheritance and unequal tactic fitness, and these two important properties of the conditional strategy hold even if negative maternal or paternal effects on progeny condition cause tactics to alternate across generations. However, the dynamics of tactic proportions pursuant to a perturbation of the equilibrium tactic proportions depend on the form of tactic inheritance. An application of our theoretical results to data from a population of smallmouth bass (Micropterus dolomieu) in which negative paternal effects dictate progeny condition reveals that age at first reproduction in males alternates regularly across generations. Furthermore, the model indicates that the population would return rapidly to equilibrium if the proportions of males that mature early or late in life were perturbed from the equilibrium within the system. This example shows how the model of the conditional strategy can be used to gain insight into tactic dynamics in situations where some of the model parameters are difficult or impossible to measure empirically.     

The contribution of the mitochondrial genome to sex‐specific fitness variance

Maternal inheritance of mitochondrial DNA (mtDNA) facilitates the evolutionary accumulation of mutations with sex‐biased fitness effects. Whereas maternal inheritance closely aligns mtDNA evolution with natural selection in females, it makes it indifferent to evolutionary changes that exclusively benefit males. The constrained response of mtDNA to selection in males can lead to asymmetries in the relative contributions of mitochondrial genes to female versus male fitness variation. Here, we examine the impact of genetic drift and the distribution of fitness effects (DFE) among mutations—including the correlation of mutant fitness effects between the sexes—on mitochondrial genetic variation for fitness. We show how drift, genetic correlations, and skewness of the DFE determine the relative contributions of mitochondrial genes to male versus female fitness variance. When mutant fitness effects are weakly correlated between the sexes, and the effective population size is large, mitochondrial genes should contribute much more to male than to female fitness variance. In contrast, high fitness correlations and small population sizes tend to equalize the contributions of mitochondrial genes to female versus male variance. We discuss implications of these results for the evolution of mitochondrial genome diversity and the genetic architecture of female and male fitness.     

RESPONSE TO NATURAL ENVIRONMENTAL HETEROGENEITY: MATERNAL EFFECTS AND SELECTION ON LIFE-HISTORY CHARACTERS AND PLASTICITIES IN MIMULUS GUTTATUS

Recent studies in plant populations have found that environmental heterogeneity and phenotypic selection vary at local spatial scales. In this study, I ask if there is evolutionary change in response to environmental heterogeneity and, if so, whether the response occurs for characters or character plasticities. I used vegetative clones of Mimulus guttatus to create replicate populations of 75 genotypes. These populations were planted into the natural habitat where they differed in mean growth, flowering phenology, and life span. This phenotypic variation was used to define selective environments. There was variation in fitness (flower production) among genotypes across all planting sites and in genotype response to the selective environment. Offspring from each site were grown in the greenhouse in two water treatments. Because each population initially had the same genetic composition, variation in the progeny between selective environments reveals either evolutionary change in response to environmental heterogeneity or environmental maternal effects. Plants from experimental sites that flowered earlier, had shorter life spans and were less productive, produced offspring that had more flowers, on average, and were less plastic in vegetative allocation than offspring of longer-lived plants from high-productivity areas. However, environmental maternal effects masked phenotypic differences in flower production. Therefore, although there was evidence of genetic differentiation in both life-history characters and their plasticities in response to small-scale environmental heterogeneity, environmental maternal effects may slow evolutionary change. Response to local-scale selective regimes suggests that environmental heterogeneity and local variation in phenotypic selection may act to maintain genetic variation.     

Detection of differential gene flow from patterns of quantitative variation

A major goal in anthropological genetics is the assessment of the effects of different microevolutionary forces. Harpending and Ward (1982) developed a model that aids in this effort by comparing observed and expected heterozygosity within populations in a local region. The expected heterozygosity within a population is a function of the total heterozygosity of the entire region and the distance of the population from the regional mean centroid of allele frequencies. Greater than average gene flow from an external source will result in a population having greater heterozygosity than expected. Less than average gene flow from an external source will result in a population having less heterozygosity than expected. We extend the Harpending-Ward model to quantitative traits using an equal and additive effects model of inheritance. Here the additive genetic variance within a population is directly proportional to heterozygosity, and its expectation is directly proportional to the genetic distance from the centroid. Under certain assumptions the expectations for phenotypic variances are similar. Observed and expected genetic or phenotypic variance can then be compared to assess the effects of differential external gene flow. When the additive genetic covariance matrix or heritabilities are not known, the phenotypic covariance matrix can be used to provide a conservative application of the model. In addition, we develop new methods for estimation of the genetic relationship matrix (R) from quantitative traits. We apply these models to two data sets: (1) six principal components derived from twenty dermatoglyphic ridge count measures for nine villages in Nepal and (2) ten anthropometric measurements for seven isolated populations in western Ireland. In both cases both the univariate and multivariate analyses provide results that can be directly interpreted in terms of historically known patterns of gene flow.     

How differing modes of non‐genetic inheritance affect population viability in fluctuating environments

Different modes of non‐genetic inheritance are expected to affect population persistence in fluctuating environments. We here analyse Caenorhabditis elegans density‐independent per capita growth rate time series on 36 populations experiencing six controlled sequences of challenging oxygen level fluctuations across 60 generations, and parameterise competing models of non‐genetic inheritance in order to explain observed dynamics. Our analysis shows that phenotypic plasticity and anticipatory maternal effects are sufficient to explain growth rate dynamics, but that a carryover model where ‘epigenetic’ memory is imperfectly transmitted and might be reset at each generation is a better fit to the data. We further find that this epigenetic memory is asymmetric since it is kept for longer when populations are exposed to the more challenging environment. Our analysis suggests that population persistence in fluctuating environments depends on the non‐genetic inheritance of phenotypes whose expression is regulated across multiple generations.     

Quantification and decomposition of environment‐selection relationships

In nature, selection varies across time in most environments, but we lack an understanding of how specific ecological changes drive this variation. Ecological factors can alter phenotypic selection coefficients through changes in trait distributions or individual mean fitness, even when the trait‐absolute fitness relationship remains constant. We apply and extend a regression‐based approach in a population of Soay sheep (Ovis aries) and suggest metrics of environment‐selection relationships that can be compared across studies. We then introduce a novel method that constructs an environmentally structured fitness function. This allows calculation of full (as in existing approaches) and partial (acting separately through the absolute fitness function slope, mean fitness, and phenotype distribution) sensitivities of selection to an ecological variable. Both approaches show positive overall effects of density on viability selection of lamb mass. However, the second approach demonstrates that this relationship is largely driven by effects of density on mean fitness, rather than on the trait‐fitness relationship slope. If such mechanisms of environmental dependence of selection are common, this could have important implications regarding the frequency of fluctuating selection, and how previous selection inferences relate to longer term evolutionary dynamics.     

Role of phenotypic plasticity and population differentiation in adaptation to novel environmental conditions

Species can adapt to new environmental conditions either through individual phenotypic plasticity, intraspecific genetic differentiation in adaptive traits, or both. Wild emmer wheat, Triticum dicoccoides, an annual grass with major distribution in Eastern Mediterranean region, is predicted to experience in the near future, as a result of global climate change, conditions more arid than in any part of the current species distribution. To understand the role of the above two means of adaptation, and the effect of population range position, we analyzed reaction norms, extent of plasticity, and phenotypic selection across two experimental environments of high and low water availability in two core and two peripheral populations of this species. We studied 12 quantitative traits, but focused primarily on the onset of reproduction and maternal investment, which are traits that are closely related to fitness and presumably involved in local adaptation in the studied species. We hypothesized that the population showing superior performance under novel environmental conditions will either be genetically differentiated in quantitative traits or exhibit higher phenotypic plasticity than the less successful populations. We found the core population K to be the most plastic in all three trait categories (phenology, reproductive traits, and fitness) and most successful among populations studied, in both experimental environments; at the same time, the core K population was clearly genetically differentiated from the two edge populations. Our results suggest that (1) two means of successful adaptation to new environmental conditions, phenotypic plasticity and adaptive genetic differentiation, are not mutually exclusive ways of achieving high adaptive ability; and (2) colonists from some core populations can be more successful in establishing beyond the current species range than colonists from the range extreme periphery with conditions seemingly closest to those in the new environment.     

Parental sex discrimination and intralocus sexual conflict

Intralocus sexual conflict occurs when populations segregate for alleles with opposing fitness consequences in the two sexes. This form of selection is known to be capable of maintaining genetic and fitness variation in nature, the extent of which is sensitive to the underlying genetics. We present a one-locus model of a haploid maternal effect that has sexually antagonistic consequences for offspring. The evolutionary dynamics of these maternal effects are distinct from those of haploid direct effects under sexual antagonism because the relevant genes are expressed only in females. Despite this, we find the same opportunity for sexually antagonistic polymorphism at the maternal effect locus as at a direct effect locus. Thus, sexually antagonistic maternal effects may underlie some natural genetic variation. The model we present permits alternative interpretations of how the genes are expressed and how the fitness variation is assigned, which invites a theoretical comparison to models of both imprinted genes and sex allocation.     

Short‐term insurance versus long‐term bet‐hedging strategies as adaptations to variable environments

Understanding how organisms adapt to environmental variation is a key challenge of biology. Central to this are bet‐hedging strategies that maximize geometric mean fitness across generations, either by being conservative or diversifying phenotypes. Theoretical models have identified environmental variation across generations with multiplicative fitness effects as driving the evolution of bet‐hedging. However, behavioral ecology has revealed adaptive responses to additive fitness effects of environmental variation within lifetimes, either through insurance or risk‐sensitive strategies. Here, we explore whether the effects of adaptive insurance interact with the evolution of bet‐hedging by varying the position and skew of both arithmetic and geometric mean fitness functions. We find that insurance causes the optimal phenotype to shift from the peak to down the less steeply decreasing side of the fitness function, and that conservative bet‐hedging produces an additional shift on top of this, which decreases as adaptive phenotypic variation from diversifying bet‐hedging increases. When diversifying bet‐hedging is not an option, environmental canalization to reduce phenotypic variation is almost always favored, except where the tails of the fitness function are steeply convex and produce a novel risk‐sensitive increase in phenotypic variance akin to diversifying bet‐hedging. Importantly, using skewed fitness functions, we provide the first model that explicitly addresses how conservative and diversifying bet‐hedging strategies might coexist.     

Genetic Allee effects on performance, plasticity and developmental stability in a clonal plant

Negative effects of small population size on fitness, so-called Allee effects, may threaten population persistence even in intact habitat remnants. We studied genotypes of 14 isolated populations of the clonal plant Ranunculus reptans, for which molecular genetic (RAPD-) variability is higher for large than for small populations. In a competition-free greenhouse environment vegetative offspring of genotypes from large populations produced more rosettes and flowers, indicating higher fitness. Within-genotype coefficients of variation in performance traits, indicating developmental instability, were lower for genotypes from populations with higher RAPD-variability. In competition with a taller grass, we found relative reduction in leaf length less pronounced for plants from large populations, suggesting higher adaptive plasticity. Our experimental study of a plant with predominantly vegetative reproduction suggests, that negative genetic effects of recent habitat fragmentation, which so far rather were expected in plants with frequent sexual reproduction, are more severe and more common than previously acknowledged.     

A general definition of the heritable variation that determines the potential of a population to respond to selection

Genetic selection is a major force shaping life on earth. In classical genetic theory, response to selection is the product of the strength of selection and the additive genetic variance in a trait. The additive genetic variance reflects a population's intrinsic potential to respond to selection. The ordinary additive genetic variance, however, ignores the social organization of life. With social interactions among individuals, individual trait values may depend on genes in others, a phenomenon known as indirect genetic effects. Models accounting for indirect genetic effects, however, lack a general definition of heritable variation. Here I propose a general definition of the heritable variation that determines the potential of a population to respond to selection. This generalizes the concept of heritable variance to any inheritance model and level of organization. The result shows that heritable variance determining potential response to selection is the variance among individuals in the heritable quantity that determines the population mean trait value, rather than the usual additive genetic component of phenotypic variance. It follows, therefore, that heritable variance may exceed phenotypic variance among individuals, which is impossible in classical theory. This work also provides a measure of the utilization of heritable variation for response to selection and integrates two well-known models of maternal genetic effects. The result shows that relatedness between the focal individual and the individuals affecting its fitness is a key determinant of the utilization of heritable variance for response to selection.     

Maternal genetic effects set the potential for evolution in a free-living vertebrate population

Heritable maternal effects have important consequences for the evolutionary dynamics of phenotypic traits under selection, but have only rarely been tested for or quantified in evolutionary studies. Here we estimate maternal effects on early-life traits in a feral population of Soay sheep (Ovis aries) from St Kilda, Scotland. We then partition the maternal effects into genetic and environmental components to obtain the first direct estimates of maternal genetic effects in a free-living population, and furthermore test for covariance between direct and maternal genetic effects. Using an animal model approach, direct heritabilities (h2) were low but maternal genetic effects (m2) represented a relatively large proportion of the total phenotypic variance for each trait (birth weight m2=0.119, birth date m2=0.197, natal litter size m2=0.211). A negative correlation between direct and maternal genetic effects was estimated for each trait, but was only statistically significant for natal litter size (ram= -0.714). Total heritabilities (incorporating variance from heritable maternal effects and the direct-maternal genetic covariance) were significant for birth weight and birth date but not for natal litter size. Inadequately specified models greatly overestimated additive genetic variance and hence direct h2 (by a factor of up to 6.45 in the case of birth date). We conclude that failure to model heritable maternal variance can result in over- or under-estimation of the potential for traits to respond to selection, and advocate an increased effort to explicitly measure maternal genetic effects in evolutionary studies.     

Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson–Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date — repeatedly described as more evolutionarily stable than expected — so this skewness should be accounted for when investigating evolutionary dynamics in the wild.     

Maternal effects provide phenotypic adaptation to local environmental conditions

In outcrossing plants, seed dispersal distance is often less than pollen movement. If the scale of environmental heterogeneity within a population is greater than typical seed dispersal distances but less than pollen movement, an individual's environment will be similar to that of its mother but not necessarily its father. Under these conditions, environmental maternal effects may evolve as a source of adaptive plasticity between generations, enhancing offspring fitness in the environment that they are likely to experience. This idea is illustrated using Campanula americana, an herb that grows in understory and light-gap habitats. Estimates of seed dispersal suggest that offspring typically experience the same light environment as their mother. In a field experiment testing the effect of open vs understory maternal light environments, maternal light directly influenced offspring germination rate and season, and indirectly affected germination season by altering maternal flowering time. Results to date indicate that these maternal effects are adaptive; further experimental tests are ongoing. Evaluating maternal environmental effects in an ecological context demonstrates that they may provide phenotypic adaptation to local environmental conditions.     

Generalists versus specialists in fluctuating environments: a bet-hedging perspective

Bet-hedging evolves in fluctuating environments because long-term genotype success is determined by geometric (rather than arithmetic) mean fitness across generations. Diversifying bet-hedging produces different specialist offspring, whereas conservative bet-hedging produces similar generalist offspring. However, many fields, such as behavioral ecology and thermal physiology, typically consider specialist versus generalist strategies only in terms of maximizing arithmetic mean fitness benefits to individuals. Here we model how environmental variability affects optimal amounts of phenotypic variation within and among individuals to maximise genotype fitness, and we disentangle the effects of individual-level optimization and genotype-level bet-hedging by comparing long-term arithmetic versus geometric mean fitness. For traits with additive fitness effects within lifetimes (e.g. foraging-related traits), genotypes of similar generalists or diversified specialists perform equally well. However, if fitness effects are multiplicative within lifetimes (e.g. sequential survival probabilities), generalist individuals are always favored. In this case, geometric mean fitness optimization requires even more within-individual phenotypic variation than does arithmetic mean fitness, causing individuals to be more generalist than required to simply maximize their own expected fitness. In contrast to previous results in the bet-hedging literature, this generalist conservative bet-hedging effect is always favored over diversifying bet-hedging. These results link the evolution of behavioral and ecological specialization with earlier models of bet-hedging, and we apply our framework to a range of natural phenomena from habitat choice to host specificity in parasites.